3r^3+8r^2=9r+5r^2

Solution for 3r^3+8r^2=9r+5r^2 equation:

Simplifying
3r3 + 8r2 = 9r + 5r2

Reorder the terms:
8r2 + 3r3 = 9r + 5r2

Solving
8r2 + 3r3 = 9r + 5r2

Solving for variable 'r'.

Reorder the terms:
-9r + 8r2 + -5r2 + 3r3 = 9r + 5r2 + -9r + -5r2

Combine like terms: 8r2 + -5r2 = 3r2
-9r + 3r2 + 3r3 = 9r + 5r2 + -9r + -5r2

Reorder the terms:
-9r + 3r2 + 3r3 = 9r + -9r + 5r2 + -5r2

Combine like terms: 9r + -9r = 0
-9r + 3r2 + 3r3 = 0 + 5r2 + -5r2
-9r + 3r2 + 3r3 = 5r2 + -5r2

Combine like terms: 5r2 + -5r2 = 0
-9r + 3r2 + 3r3 = 0

Factor out the Greatest Common Factor (GCF), '3r'.
3r(-3 + r + r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

Move all terms containing r to the left, all other terms to the right.

Simplifying
r = 0
Subproblem 2
Set the factor '(-3 + r + r2)' equal to zero and attempt to solve:

Simplifying
-3 + r + r2 = 0

Solving
-3 + r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + r + 3 + r2 = 0 + 3

Reorder the terms:
-3 + 3 + r + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + r + r2 = 0 + 3
r + r2 = 0 + 3

Combine like terms: 0 + 3 = 3
r + r2 = 3

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
r + 0.25 + r2 = 3 + 0.25

Reorder the terms:
0.25 + r + r2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + r + r2 = 3.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(r + 0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
r + 0.5 = 1.802775638

Simplifying
r + 0.5 = 1.802775638

Reorder the terms:
0.5 + r = 1.802775638

Solving
0.5 + r = 1.802775638

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 1.802775638 + -0.5
r = 1.802775638 + -0.5

Combine like terms: 1.802775638 + -0.5 = 1.302775638
r = 1.302775638

Simplifying
r = 1.302775638

Subproblem 2
r + 0.5 = -1.802775638

Simplifying
r + 0.5 = -1.802775638

Reorder the terms:
0.5 + r = -1.802775638

Solving
0.5 + r = -1.802775638

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -1.802775638 + -0.5
r = -1.802775638 + -0.5

Combine like terms: -1.802775638 + -0.5 = -2.302775638
r = -2.302775638

Simplifying
r = -2.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.302775638, -2.302775638}
Solution
r = {0, 1.302775638, -2.302775638}